Continuous-Time Analog Filtering: Design Strategies and Programmability in CMOS Technologies for VHF Applications 171 control the HS transconductance from 270 to 452 μA/V, and changes from 40 to 100 μA in the FC topology control the transconductance from 550 to 800 μA/V. 200 250 300 350 400 450 -450 -350 -250 -150 -50 50 150 250 350 450 V c (mV) IBIAS=180uA IBIAS=135uA IBIAS=90uA IBIAS=45uA 480 520 560 600 640 680 720 760 800 -140 -105 -70 -35 0 35 70 105 140 V c (mV) IBIAS=100uA IBIAS=80uA IBIAS=60uA IBIAS=40uA (a) (b) Fig. 15. Transconductance versus biasisng currents (fine tuning) for the: (a) HS implementation; (b) FC implementation. To conclude, the proposed structure is a balanced topology aimed at improving immunity to digital noise and linearity. A digitally programmable transconductor has been designed, maintaining the same dynamic range over the entire frequency range. Therefore, it can be used in the design of programmable filters, as the expected characteristics of a programmable cell will be obtained: to maintain Q-factor, noise power and maximum signal swing constant over the entire programming range, leading to a DR independent on the operation frequency. The expected linear dependence of the unity-gain frequency is obtained and the phase error is effectively reduced over the entire programming range in both implementations, with a compensation scheme based on two cross-coupled capacitors for the HS topology and the classical RC circuit connected at the input for the FC approach. 8. Results and discussion To demonstrate the theoretical advantages of this approach for a programmable transconductor suitable for VHF, two 3-bit programmable integrators have been designed. The HS transconductor has been implemented by using the design kit of an AMI Semiconductor (AMIS) 0.35 μm CMOS technology (P-substrate, N-well, 5-metal, 2-poly) with a 3 V power supply and a nominal bias current of 90 μA per branch; whereas the FC transconductor has been implemented by using the design kit of an AMS (C35B4C3) 0.35 μm CMOS technology (P-substrate, N-well, 4-metal, 2-poly) with a 2 V power supply and a nominal bias current of 100 μA per branch. The dimensions of the transistors were chosen in order to cover all the design requirements obtained in this chapter, leading to a complete sweep of the discrete step by varying the bias current. In this way, for the HS implementation, the operation point is located at 90 μA and the bias current adjustment is possible from 45-180 μA. However, for the FC implementation, the operating point is located at 100 μA, covering the digital step by varying the bias current from 20-110 μA. In this way, the discrete tunability requirement is obtained but the FC transconductance value at the operation point is maximised. 8.1 Layout strategy A careful layout has been drawn out to obtain all the characteristics associated with the proposed design accurately and demonstrate the feasibility of the intended approach. As g m (μA/V) g m (μA/V) Advances in Solid State Circuits Technologies 172 stated below, we have taken special care to get rid of the unwanted effects related to parasitic elements and mismatching (Baker et al., 1998; Hastings, 2001). All the designs have been carried out taking into account the specific design rules for high frequency operation, which are highly appropriate for obtaining good matching between components. Interdigitized and common-centroid layout techniques have been considered to reduce the variations of threshold voltage, which are associated with gradients in gate-oxide thickness. Guard rings have been included in the design with the aim of reducing substrate noise. Bond-pads have also been carefully laid out and, in this way, input and output pins have been placed as far as possible between them. Balanced structures provide outstanding benefits, but they are strongly dependent on the symmetry of the circuit. Consequently, special care has been taken to outline the paths of the balanced signals, in an attempt to ensure the best matching between them. MOS devices have fragile gates seeing that electrostatic discharges may cause destruction of the device if the oxide breakdown voltage is exceeded. Considering this point, we concluded that it would be advisable to provide the transistors that control the quality factor of the circuit with a path protection system. The scheme chosen to achieve this goal was the anti-parallel diodes configuration. This circuit is very straightforward and simple but is sufficient for the purposes of this work. Fig. 16(a) shows the drawn layout of the HS test chip with an active area of 0.10 mm 2 . Fig. 16(b) shows the microphotograph of the programmable FC transconductor, with an active area of 0.04 mm 2 including the compensation RC circuit, where the integration capacitance has been implemented with a double-poly capacitor. The area of the FC active element is 0.03 mm 2 and a regular and compact arrangement of transistors can be observed. (a) (b) Fig. 16. (a) Layout of the fully-balanced 3-bit programmable HS integrator. (b) Microphotograph of the FC integrator, by using double-poly capacitors. 8.2 Experimental results For the HS approach, a unity-gain frequency of 28 MHz was achieved with a power dissipation of 1.62 mW using a 3 V supply. By varying the digital word from 1 to 7, we expected to control the unity-gain frequency from 28 to 185 MHz and the experimental results lead to a variation between 25 and 185 MHz, as shown in Fig. 17(a). Focusing on the b 2 b 1 b 0 Continuous-Time Analog Filtering: Design Strategies and Programmability in CMOS Technologies for VHF Applications 173 same figure, by varying the bias current source from 45 to 180 μA for a fixed digital word, the transconductance value is modified, providing complementary fine tuning of the frequency. All discrete steps are covered and, in consequence, a frequency span of 25-185 MHz can be provided. The maximum frequency error is obtained at the maximum digital word where a deviation of 6 % is obtained from the 7:1 ratio. 10 50 90 130 170 210 250 290 45 65 85 105 125 145 165 185 7gm 6gm 5gm 4gm 3gm 2gm 1gm 20 40 60 80 100 120 140 160 180 200 220 20 30 40 50 60 70 80 90 100 110 5gm 4gm 3gm 2gm 1gm (a) (b) Fig. 17. Experimental results for coarse and fine tuning of the (a) HS and (b) FC topology. Variation of the unity-gain frequency versus bias currents for all the digital words. For the FC approach, a unity-gain frequency of 40 MHz is achieved with a power dissipation of 2.4 mW using a 2 V supply, as expected from the post-layout simulation results. By varying the digital word from 1 to 5, the unity-gain frequency is controlled from 40 to 190 MHz, as shown in Fig. 17(b). All discrete steps are swept by varying the bias current from 20 to 110 μA. The maximum frequency error is obtained at the maximum digital word where a deviation of 5 % is obtained from the 5:1 ratio. The next step is to demonstrate constant linearity by means of a constant THD over the entire programming range. Figs. 18 and 19 show the THD variation as a function of the differential output current for all the digital words. THD was measured for a sine input current of 10 MHz (a) and for the unity-gain frequency (b) in both topologies. These figures show the expected THD dependence, studied above in section §6: lower bias currents or higher input signal amplitudes lead to higher THD values. A corner parameter analysis was carried out following the guidelines provided by the design kit manufacturer of the ‘AMI Semiconductor C035M Design-Kit’ and the worst-case analysis for the HS integrator was obtained. This distortion study gave 1 % of THD for a differential input signal of 56 μA and 10 MHz. Experimental results for the design, shown in Fig. 18, lead to a differential input current of 50 μA in the same situation. For the FC approach, the expected value for 1 % of THD was a differential input signal amplitude of 37 μA and 10 MHz; and the experimental results (Fig. 19), give an amplitude of 35 μA. The post-layout simulated result for the input-referred noise integrated from 0 to 30 MHz in the HS topology was 11.2 nA rms . Hence, the dynamic range, defined as the input signal amplitude at 1 % THD divided by the total noise level integrated over 30 MHz, is 70 dB. In the FC structure, the input-referred noise integrated from 0 to 40 MHz was 8 nA rms . Hence, the dynamic range, defined as the input signal amplitude at 1 % THD divided by the total noise level integrated over 40 MHz, is also 70 dB. In summary, frequency is adjusted in a coarse discrete way by connecting identical transconductors in parallel and with fine continuous tuning by varying the biasing current. ω t (MHz) I bias ( μ A) ω t (MHz) I bias ( μ A) Advances in Solid State Circuits Technologies 174 -60 -56 -52 -48 -44 -40 -36 0 0,04 0,08 0,12 0,16 0,2 0,24 0,28 iout/Ibias THD(dB) @ 10MHz 4gm 2gm gm -70 -65 -60 -55 -50 -45 -40 -35 0,04 0,12 0,20 0,28 0,36 0,44 iout/Ibias THD(dB) @ Wt=25 MHz 4gm 2gm gm (a) (b) Fig. 18. THD versus differential output current in the HS integrator for three different digital words: (a) ω(input)=10 MHz, (b) ω(input)= ω t (25 MHz for 1g m ). -65 -60 -55 -50 -45 -40 -35 0,04 0,08 0,12 0,16 iout/Ibias THD(dB) @ 10 MHz gm 2gm 3gm 4gm 5gm -65 -60 -55 -50 -45 -40 -35 0,04 0,08 0,12 0,16 0,2 0,24 iout/Ibias THD(dB) @ Wt=40 MHz gm 2gm 3gm 4gm 5gm (a) (b) Fig. 19. THD versus differential output current in the FC integrator for all the digital words: (a) ω(input)=10 MHz, (b) ω(input)= ω t (40 MHz for 1g m ). The feasibility of the programmable array of transconductors has been proven in a 3-bit programmable integrator obtaining frequency scaling as expected. All the specifications in both transconductor implementations are summarized in table 7. The main advantage of the topology proposed was the inherent enhancement of the dc-gain, provided through the existing positive feedback compensation (negative resistance). The HS design condition was very difficult to achieve because technological process and temperature variations are expected to be greater than the small changes required in this topology. As expected, by varying the external control for this negative resistance, no change was obtained for the dc-gain. The post-layout simulated dc-gain was a variation of 15 dB between the minimum (40 dB) and the maximum (55 dB), with a maximum CMRR of 60 dB. The experimental results lead to a differential dc-gain of 30 dB with no change with the value of the negative resistance and a CMRR greater than 35 dB over the entire frequency range. Therefore, in this case, there is no control on the dc-gain of the system. The design condition for the FC topology is less restrictive and two different implementations have been fabricated. The post-layout simulation results in both cases showed a dc-gain control of 15 dB from 30 to 45 dB and a maximum CMRR of 50 dB. The first implementation has been designed with the same dimensions for the M N transistors Continuous-Time Analog Filtering: Design Strategies and Programmability in CMOS Technologies for VHF Applications 175 involved in the negative resistance, and similar results are obtained as in the HS topology. There is no external dc-gain control and an experimental value of 26 dB and CMRR of 33 dB are obtained. In the second one, where a pre-designed mismatching is included between M N transistors involved in the negative resistance, a variation of 12 dB (from 26 to 38 dB) for the dc-gain is obtained by modifying the value of the negative resistance (Fig. 20). The CMRR is greater than 46 dB over the entire frequency range. HS topology FC topology Power supply voltage 3 V 2 V Unity-gain frequency 25 MHz 40 MHz Power dissipation 1.62 mW 2.4 mW CMRR over the entire pass-band >35 dB >46 dB Active area 0.10 mm 2 0.04 mm 2 Total rms input-referred noise (sim.) 11.2 nA rms 8 nA rms Maximum differential input signal current at 1 % THD @ 10 MHz 50 μA (peak) 35 μA (peak) Dynamic range 70 dB 70 dB Table 7. Summary of the experimental results for the integrator (1 LSB). -25 -15 -5 5 15 25 35 0 1 10 100 1000 frequency ( MHz) gain (dB) Fig. 20. Experimental dc-gain control for the FC transconductor with a pre-designed mismatching between M N transistors involved in the negative resistance. 9. Conclusion This work describes a new approach for implementing digitally programmable and continuously tunable VHF/UHF transconductors compatible with pure digital CMOS technologies and suitable for HDD read channel applications. The cell is suitable for low- voltage operation over an extended frequency range. The programmability exhibited by the transconductor is due to the use of a generic programmable structure that gives a G m digital control as a parallel connection of unit cells, and the total parasitic capacitances are maintained constant thanks to the specific design of the unit cell: a cascode stage with 12 dB Advances in Solid State Circuits Technologies 176 dummy elements. This transconductor could be used in any kind of G m -C filter, thus providing a very wide range of programmable CT filters. The fully-balanced current-mode G m -C integrator based on this topology exhibits a unity-gain frequency programmability from 25-185 MHz in the HS implementation and 40-200 MHz in the FC approach; with a phase error of less than 4º in both topologies throughout the entire operating frequency range. Total harmonic distortion (THD) of less than 1 % (-40 dB) for a differential input signal of 50 and 35 μA in the HS and FC topology respectively is obtained. The integrator operates over the programming range with 70 dB of dynamic range for 1 % of THD. The cell has been fabricated in a 0.35 μm CMOS process. The experimental results confirm this approach as an excellent choice to achieve filters exhibiting a good trade-off between tuning capability and dynamic range working in the very high frequency range. The proposed technique can be easily adapted to lower power supply voltages by using folded cascode structures and, in addition, better frequency ranges of operation can be achieved considering current CMOS digital technologies. 10. References Abidi A. (1988). On the Operation of Cascode Gain Stages. IEEE Journal of Solid-State Circuits, Vol. 23, No. 6, 1988, 1434-1437, ISSN: 0018-9200. Ahn H.T. & Allstot D. J. (2002). A 0.5-8.5 GHz Fully-Differential CMOS Distributed Amplifier. IEEE Journal of Solid-State Circuits, Vol. 37, No. 8, August 2002, 985-988, ISSN: 0018-9200. Baker R.J.; Li H.W. & Boyce D.E. (1998). CMOS Circuit Design, Layout and Simulation. IEEE Press Series on Microelectronic Systems, 1998. Baschirotto A.; Rezzi F. & Castello R. (1994). Low-Voltage Balanced Transconductor with High Input Common-Mode Rejection. Electronics Letters, Vol. 30, No. 20, September 1994, 1669-1671, ISSN: 0013-5194. Bollati G.; Marchese S.; Demicheli M. & Castello R. (2001). An Eight-Order CMOS Low-Pass Filter with 30-120 MHz Tuning Range and Programmable Boost. IEEE Journal of Solid-State Circuits, Vol. 36, No. 7, July 2001, 1056-1066, ISSN: 0018-9200. Croon J.A.; Rosmeulen M.; Decoutere S.; Sansen W. & Maes H.E. (2002). An Easy-to-Use Mismatch Model for the MOS Transistor. IEEE Journal of Solid-State Circuits, Vol. 37, No. 8, August 2002, 1056-1064, ISSN: 0018-9200. Felt E.; Narayan A. & Sangiovanni-Vincentelli A. (1994). Measurement and Modelling of MOS Transistors Current Mismatch in Analog ICs, Proceedings of the IEEE/ACM International Conference on Computer Aided Design, pp. 272-277, ISBN: 0-8186-6417-7, San Jose, California, November 1994, Broadway, New York. Gray P.R. & Meyer R.G. (2001). Analysis and Design of Analog Integrated Circuits, 4 th Edition, John Wiley & Sons, Inc., 2001. Gregor R.W. (1992). On the Relationship Between Topography and Transistor Matching in an Analog CMOS Technology. IEEE Transactions on Electron Devices, Vol. 39, No. 2, 1992, 275-282, ISSN: 0018-9383. Hastings A. (2001). The Art of Analog Layout, Prentice Hall, Inc., 2001. Continuous-Time Analog Filtering: Design Strategies and Programmability in CMOS Technologies for VHF Applications 177 Mohan S.S.; Hershenson M.; Boyd S.P. & Lee T.H. (2000). Bandwidth Extension in CMOS with Optimized On-Chip Inductors. IEEE Journal of Solid-State Circuits, Vol. 53, No. 3, March 2000, 346-355, ISSN: 0018-9200. Nauta B. (1993). Analog CMOS Filters for Very High Frequencies, Kluwer Academic Publishers, 1993. Otín A.; Celma S. & Aldea C. (2004). Digitally Programmable CMOS Transconductor for Very High Frequency. Microelectronics Reliability Journal, Vol. 44, No. 5, 2004, pp. 869-875, ISSN: 0026-2714. Otín A.; Celma S. & Aldea C. (2005). A 0.18 μm CMOS 3 rd -order Digitally Programmable G m -C Filter for VHF Applications. IEICE Transactions on Information and Systems, Vol. E88-D, No. 7, July 2005, 1509-1510, ISSN: 0916-8532. Pavan S. & Tsividis Y.P. (2000). High Frequency Continuous Time Filters in Digital CMOS Processes, Kluwer Academic Publishers, London, 2000. Pavan S. & Tsividis Y.P. (2000). Widely Programmable High-Frequency Continuous-Time Filters in Digital CMOS Technology. IEEE Journal of Solid-State Circuits, Vol. 35, No. 4, 2000, 503-511, ISSN: 0018-9200. Pelgrom M.J.M.; Duinmaijer A.C.J. & Welbers A.P.G. (1989). Matching Properties of MOS Transistors. IEEE Journal of Solid-State Circuits, Vol. 24, No. 5, October 1989, 1433- 1440, ISSN: 0018-9200. Säckinger E. & Fischer W.C. (2000). A 3 GHz 32 dB CMOS Limiting Amplifier for SONET OC-48 Receivers. Proceedings of the International Solid-State Circuits Conference, Digest of Technical Papers, pp. 158-159, ISBN: 0-7803-5855-4, San Francisco CA, February 2000, IEEE Service Center, P.O. Box 1331, Piscataway. Sansen W.; Huijsing J. & De Plassche R. (1999). Analog Circuit Design, Kluwer Academic Publishers, 1999. Sedra A.S. & Smith K.C. (2004). Microelectronic Circuits, Fifth-Edition, Oxford University Press, Inc., New York, 2004. Silva-Martínez J.; Steyaert M. & Sansen W. (2003). High-Performance CMOS Continuous-Time Filters, Kluwer Academic Publishers, 2003. Smith S.L. & Sánchez-Sinencio E. (1996). Low Voltage Integrators for High-Frequency CMOS Filters using Current Mode Techniques. IEEE Trans. on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 43, No.1, 1996, 39-48, ISSN: 1057-7130. Tsividis Y.P. (1996). Mixed Analog Digital VLSI Devices and Technology, McGraw-Hill, New York, 1996. Tsividis Y.P. (1999). Operation and Modeling of the MOS Transistor, 2 nd Edition, McGraw-Hill, New York, 1999. Vadipour M. (1993). A New Compensation Technique for Resistive Level Shifters. IEEE Journal of Solid-State Circuits, Vol. 28, No. 1, January 1993, 93-95, ISSN: 0018-9200. Wakimoto T. & Akazawa Y. (1990). A Low-Power Wide-Band Amplifier Using a New Parasitic Capacitance Compensation Scheme. IEEE Journal of Solid-State Circuits, Vol. 25, No. 1, February 1990, 200-206, ISSN: 0018-9200. Wyszynski A. & Schaumann R. (1994). Avoiding Common-Mode Feedback in Continuous- Time G m -C Filters by the Use of Lossy-Integrators. Proceedings of the IEEE Advances in Solid State Circuits Technologies 178 International Symposium on Circuits and Systems, Vol. 5, pp. 281, Vancouver (Canada), May 1994. Zele R.H. & Allstot D. (1996). Low-Power CMOS Continuous-Time Filters. IEEE Journal of Solid-State Circuits, Vol. 31, No. 2, 1996, 157-168, ISSN: 0018-9200. 9 Impact of Technology Scaling on Phase-Change Memory Performance Stefania Braga, Alessandro Cabrini and Guido Torelli Department of Electronics, University of Pavia Italy 1. Introduction Nowadays, non-volatile storage technologies play a fundamental role in the semiconductor memory market due to the widespread use of portable devices such as digital cameras, MP3 players, smartphones, and personal computers, which require ever increasing memory capacity to improve their performance. Although, at present, Flash memory is by far the dominant semiconductor non-volatile storage technology, the aggressive scaling aiming at reducing the cost per bit has recently brought the floating-gate storage concept to its technological limit. In fact, data retention and reliability of floating-gate based memories are related to the thickness of the gate oxide, which becomes thinner and thinner with increasing downscaling. The above limit has pushed the semiconductor industry to invest on alternatives to Flash memory technology, such as magnetic memories, ferroelectric memories, and phase change memories (PCMs) (Geppert, 2003). The last technology is one of the most interesting candidates due to high read/write speed, bit-level alterability, high data retention, high endurance, good compatibility with CMOS fabrication process, and potential of better scalability. However, it still requires strong efforts to be optimized in order to compete with Flash technology from the cost and the performance points of view. In PCMs, information is stored by exploiting two different solid-state phases (namely, the amorphous and the crystalline phase) of a chalcogenide alloy, which have different electrical resistivity (more specifically, the resistivity is higher for the amorphous, or RESET, phase and lower for the crystalline, or SET, phase). Phase transition is a reversible phenomenon, which is achieved by stimulating the cell by means of adequate thermal pulses induced by applying electrical pulses. Reading the resistance of any programmed cell is achieved by sensing the current flowing through the chalcogenide alloy under predetermined bias voltage conditions. The read window, that is, the range from the minimum (RESET) to the maximum (SET) read current, is considerably wide, which allows safe storage of an information bit in the cell and also opens the way to the multi-level approach to achieve low-cost high-density storage. ML storage consists in programming the memory cell to one in a plurality of intermediate resistance (i.e., of read current) levels inside the available window, which allows storing more than one bit per cell (the number of bits that can be stored in a single cell is n = log 2 m, where m is the number of programmable levels). The programming power and the read window depend on the electrical properties of the cell materials as well as on the architecture and the size of the memory cell. As the fabrication Advances in Solid State Circuits Technologies 180 technology scales down the cell dimensions, new challenges arise to accurately program the cell to intermediate states and discriminate adjacent resistance levels. In this work, we investigate the impact of technology scaling down on both the program and the read operation by means of a simple analytical model which takes the electro- thermal behavior of the PCM cell and the phase change phenomena inside the chalcogenide alloy into account. 2. Working principle of the PCM cell The working principle of a PCM cell relies on the physical properties of chalcogenide materials, typically Ge 2 Sb 2 Te 5 (GST), that can switch from the amorphous to the crystalline phase and vice versa when stimulated by suitable electrical pulses. Basically, a PCM cell is composed of a thin GST film, a resistive element named heater (TiN), and two metal electrodes, i.e., the top electrode contact (TEC) and the bottom electrode contact (BEC). Only a portion of the GST layer, which is located close to the GST-heater interface and is referred to as active GST, undergoes phase transition when the PCM cell is thermally stimulated. In particular, in this work we focus our attention on the Lance heater geometry (Pellizzer et al., 2006), which is essentially composed of a thin layer of GST alloy and a pillar-shaped heater, as shown in Fig. 1. In the reference Lance heater cell implemented in the 90 nm technology node, the GST thickness t is 70 nm, the GST-heater contact area A is 3000 nm 2 , and the heater height h is 180 nm. The typical V-I characteristic of the PCM cell in the amorphous (RESET) and the crystalline (SET) state is shown in Fig. 2. Consider the case of a cell in its full-SET state: the differential resistance of the cell decreases as the applied voltage increases. This effect is due to the contribution of the crystalline GST to the cell resistance. In fact, the crystalline GST resistivity decreases with increasing electrical field inside the material. GST h t Heater z-axis A Fig. 1. Conceptual scheme of a PCM Lance heater cell. [...]... 90ănm node and beyond, Solid- State Electronics 52(9): 14 67 – 1 472 192 Advances in Solid State Circuits Technologies Thomas, C B., Rogers, B D & Lettington, A H (1 976 ) Monostable switching in amorphous chalcogenide semiconductors, Journal of Physics D: Applied Physics 9(18): 2 571 –2586 Weidenhof, V., Pirch, N., Friedrich, I., Ziegler, S &Wuttig, M (2000) Minimum time for laser induced amorphization of... nm, 70 nm, and 100 nm (b) Notice that the temperature profile is almost linear inside the GST layer The maps were obtained by means of our 3D electro-thermal model (Braga et al., 2008) Isotropic scaling 70 0 500 500 400 400 300 m m 600 I (μA) 600 I (μA) Shrinking 70 0 300 200 200 100 100 0 0 0.2 0.4 0.6 Scaling factor ε 0.8 1 0 0 0.2 0.4 0.6 Scaling factor ε 0.8 1 Fig 6 Melting current reduction in the... need In this way, a good convergence will meet The commands in Fig.3a will cause convergence problems in a great probability while commands in Fig.3b always provide good convergence In the snapback region of ESD protection structure, the current increase rapidly Thus, in the simulation, a small ΔV will induce a large ΔI which induces the simulation failing to converge Aiming at soling this problem, a particular... Project RBAP06L4S5 7 References Adler, D., Shur, M S., Silver, M & Ovshinsky, S R (1980) Threshold switching in chalcogenide-glass thin films, Journal of Applied Physics 51(6): 3289–3309 Braga, S., Cabrini, A & Torelli, G (2008) An integrated multi-physics approach to the modeling of a phase-change memory device, Proc of Solid- State Device Research Conference, pp 154–1 57 Braga, S., Cabrini, A & Torelli,... of melting current reduction in the cases of isotropic scaling and shrinking is shown in Fig 6 In order to compare PCM cells having different dimensions, we chose to consider the fullRESET state to be achieved when the maximum temperature inside the PCM cell reaches a 185 Impact of Technology Scaling on Phase-Change Memory Performance Fig 5 Cell structure (a) and simulated temperature Maps inside a... 2008) In the following, we will consider heater geometries with a high aspect ratio with the purpose of investigating the scaling perspective, even if they may require advanced fabrication techniques Given a scaling factor ε < 1, Im turns out to be proportional to ε in the case of isotropic scaling, where all the linear dimensions are scaled by the same amount, while Im ∝ ε2 in the case of shrinking,... provided in the simulator as shown in Fig.4 A series resistor is put together with the ESD protection structure Therefore, the current can be written as: I= (Vout -Vinternal)/R, and in this way, a small ΔI can be gained, which will improve the convergence In the simulation of ESD events, this method must be included, and generally the value for R is set to be larger than 1×1 07 Ω 200 Advances in Solid State. .. from taking place The minimum current required to melt a portion of the active GST layer is referred to as melting current, Im When the current flowing through the memory cell during a write operation is higher than Im, the obtained RESET resistance increases with the amplitude of the current pulse In fact, the maximum temperature inside the cell increases with the pulse amplitude, thus leading to the... melting point As pointed out above, the temperature profile along the cell axis inside the GST decreases almost linearly with the distance from the GST-heater interface By approximating the thermal profile inside the GST along the cell axis with a straight line, we derived the analytical expression for the thickness of the amorphous cap xa obtained when a full-RESET pulse is applied to the cell: 188 Advances. .. Fig.2, it is easy to find that all calculations are based on an initial guess And a bad initial guess will surely induce convergence problem This case often happens on two occasions Sometimes, the simulation should be divided into subsections, and in some regions small value for “initialstep” should be used to obtain a good initial guess while in other regions large value for “initialstep” should be . level integrated over 40 MHz, is also 70 dB. In summary, frequency is adjusted in a coarse discrete way by connecting identical transconductors in parallel and with fine continuous tuning by. the case of shrinking, where only planar dimensions are scaled. The comparison of melting current reduction in the cases of isotropic scaling and shrinking is shown in Fig. 6. In order to compare. 0.8 1 0 100 200 300 400 500 600 70 0 Shrinking Scaling factor ε I m (μA) Fig. 6. Melting current reduction in the case of isotropic scaling (left) and shrinking (right). The dimensions are